Question

Distance moved by a charged particle in magnetic field (with parallel velocity component) in one rotation is:

• A. \( \frac{2 \pi m v}{q B} \)
• B. \( \frac{m v}{q B} \)
• C. \( \frac{4 \pi m v}{q B} \)
• D. \( \frac{2 \pi m v}{q B^2} \)

Hint:

For helical motion, axial distance per rotation is \( v_{\parallel} \cdot T \), where \( T = \frac{2\pi m}{qB} \).

Answer 1

The Correct Option is A

Helical path: distance in 1 rotation = pitch = \( v_{\parallel} \cdot T \),
where \( T = \frac{2 \pi m}{qB} \) and \( v = v_{\parallel} \Rightarrow \text{Distance} = v \cdot \frac{2 \pi m}{qB} = \frac{2 \pi m v}{q B} \)